EXPERIMENTALLY OBTAINED BIFURCATION PHENOMENON IN CHAOTIC TRACTOR VIBRATING IN TIME AND FREQUENCY DOMAIN

2005 ◽  
Vol 15 (01) ◽  
pp. 225-231 ◽  
Author(s):  
L. O. GARCIANO ◽  
K. SAKAI ◽  
R. TORISU
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Period Doubling ◽  
Nonlinear Resonance ◽  
Nonlinear Time Series ◽  
Continuous Wavelet ◽  
Bifurcation Phenomenon ◽  
Dominant Feature ◽  
Positive Exponent

This paper investigates through experimental methods the dynamic characteristics of a farm tractor by changing the forward velocity from 0.63 m/s to 4.50 m/s. Nonlinear time series, frequency spectrum and continuous wavelet transform were used in the analysis. From the nonlinear time series analysis, a nonlinear resonance of the tractor vibration occurred at forward velocity of 2.15 m/s. The existence of a subharmonic frequency at 4.32 m/s indicated chaotic dynamics that was confirmed by the trend of the Lyapunov exponent analysis with a positive exponent indicating chaos. Continuous wavelet transform analysis results, presented graphically, called coefficient plots showed patterns composed of large and fine feature distribution in both time and scale. Quasi-periodic velocities of 1.95 m/s and 2.15 m/s were estimated by these coefficient plots. At forward velocity of 2.88 m/s, the coefficient plots showed dominant features that varied periodically and were estimated to be a period-doubling vibration. The coefficient plots during chaotic vibration at 3.52 m/s, 4.02 m/s and 4.32 m/s showed various feature distributions. At forward velocities of 0.95 m/s and 1.42 m/s, the existence of features with scale values of almost equal and half of the dominant feature was due to the influence of the gravel road surface and not to the artificial test track profile. Experimentally obtained bifurcation was observed clearly from the coefficient plots that showed three different patterns from quasi-periodic vibration at 2.15 m/s, period-doubling at 2.88 m/s and chaos at 3.52 m/s.

scholarly journals Time-space characterization of droughts in the São Francisco river catchment using the Standard Precipitation Index and continuous wavelet transform

RBRH ◽  
2019 ◽  
Vol 24 ◽  
Author(s):  
Marcus Suassuna Santos ◽  
Veber Afonso Figueiredo Costa ◽  
Wilson dos Santos Fernandes ◽  
Rafael Pedrollo de Paes
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Large Scale ◽  
Continuous Wavelet ◽  
River Catchment ◽  
Time Space ◽  
L Moments ◽  
Space Characterization

ABSTRACT This paper focuses on time-space characterization of drought conditions in the São Francisco River catchment, on the basis of wavelet analysis of Standardized Precipitation Index (SPI) time series. In order to improve SPI estimation, the procedures for regional analysis with L-moments were employed for defining statistically homogeneous regions. The continuous wavelet transform was then utilized for extracting time-frequency information from the resulting SPI time series in a multiresolution framework and for investigating possible teleconnections of these signals with those obtained from samples of the large-scale climate indexes ENSO and PDO. The use of regional frequency analysis with L-moments resulted in improvements in the estimation of SPI time series. It was observed that by aggregating regional information more reliable estimates of low frequency rainfall amounts were obtained. The wavelet analysis of climate indexes suggests that the more extreme dry periods in the study area are observed when the cold phase of both ENSO and the PDO coincides. While not constituting a strict cause effect relationship, it was clear that the more extreme droughts are consistently observed in this situation. However, further investigation is necessary for identifying particularities in rainfall patterns that are not associated to large-scale climate anomalies.

scholarly journals A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis

2018 ◽  
Vol 25 (1) ◽  
pp. 175-200 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform equivalent of the extended Lomb–Scargle periodogram defined in Part 1 of this study (Lenoir and Crucifix, 2018). The signal being analysed is modelled as the sum of a locally periodic component in the time–frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighbouring times in order to reduce its variance. The Shannon–Nyquist exclusion zone is however defined as the area corrupted by local aliasing issues. The local amplitude in the time–frequency plane is then estimated with least-squares methods. We also derive an approximate formula linking the squared amplitude and the scalogram. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

scholarly journals RAINFALL ANALYSIS IN KLANG RIVER BASIN USING CONTINUOUS WAVELET TRANSFORM

2016 ◽  
Vol 10 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Celso A. G. Santos ◽  
Richarde Marques Silva ◽  
Seyed Ahmad Akrami
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
River Basin ◽  
Continuous Wavelet Transform ◽  
Rainfall Data ◽  
Accurate Information ◽  
Rainfall Time Series ◽  
Continuous Wavelet ◽  
Rainfall Analysis ◽  
Frequency Components

The rainfall characteristics within Klang River basin is analyzed by the continuous wavelet transform using monthly rainfall data (1997–2009) from a raingauge and also using daily rainfall data (1998–2013) from the Tropical Rainfall Measuring Mission (TRMM). The wavelet power spectrum showed that some frequency components were presented within the rainfall time series, but the observed time series is short to provide accurate information, thus the daily TRMM rainfall data were used. In such analysis, two main frequency components, i.e., 6 and 12 months, showed to be present during the entire period of 16 years. Such semiannual and annual frequencies were confirmed by the global wavelet power spectra. Finally, the modulation in the 8–16-month and 256–512-day bands were examined by an average of all scales between 8 and 16 months, and 256 and 512 days, respectively, giving a measure of the average monthly/daily variance versus time, where the periods with low or high variance could be identified.

scholarly journals A general theory on frequency and time-frequency analysis of irregularly sampled time series based on projection methods. II. Extension to time-frequency analysis

2017 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform-equivalent of the extended Lomb-Scargle periodogram defined in part I of this study (Lenoir and Crucifix, 2017). The signal being analyzed is modeled as the sum of a locally periodic component in the time-frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighboring times in order to reduce its variance. The Shannon-Nyquist exclusion zone is on the other hand defined as the area corrupted by local aliasing issues. The local amplitude in the time-frequency plane is then estimated with least-squares methods. We show that the squared amplitude and the scalogram are approximately proportional. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov Chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

scholarly journals Integrating the Continuous Wavelet Transform and a Convolutional Neural Network to Identify Vineyard Using Time Series Satellite Images

2019 ◽  
Vol 11 (22) ◽  
pp. 2641 ◽  
Author(s):  
Longcai Zhao ◽  
Qiangzi Li ◽  
Yuan Zhang ◽  
Hongyan Wang ◽  
Xin Du
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Continuous Wavelet Transform ◽  
Satellite Images ◽  
Vegetation Index ◽  
Continuous Wavelet ◽  
Crop Types ◽  
Reconstructed Time Series

Grape is an economic crop of great importance and is widely cultivated in China. With the development of remote sensing, abundant data sources strongly guarantee that researchers can identify crop types and map their spatial distributions. However, to date, only a few studies have been conducted to identify vineyards using satellite image data. In this study, a vineyard is identified using satellite images, and a new approach is proposed that integrates the continuous wavelet transform (CWT) and a convolutional neural network (CNN). Specifically, the original time series of the normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), and green chlorophyll vegetation index (GCVI) are reconstructed by applying an iterated Savitzky-Golay (S-G) method to form a daily time series for a full year; then, the CWT is applied to three reconstructed time series to generate corresponding scalograms; and finally, CNN technology is used to identify vineyards based on the stacked scalograms. In addition to our approach, a traditional and common approach that uses a random forest (RF) to identify crop types based on multi-temporal images is selected as the control group. The experimental results demonstrated the following: (i) the proposed approach was comprehensively superior to the RF approach; it improved the overall accuracy by 9.87% (up to 89.66%); (ii) the CWT had a stable and effective influence on the reconstructed time series, and the scalograms fully represented the unique time-related frequency pattern of each of the planting conditions; and (iii) the convolution and max pooling processing of the CNN captured the unique and subtle distribution patterns of the scalograms to distinguish vineyards from other crops. Additionally, the proposed approach is considered as able to be applied to other practical scenarios, such as using time series data to identify crop types, map landcover/land use, and is recommended to be tested in future practical applications.

scholarly journals RAINFALL ANALYSIS IN KLANG RIVER BASIN USING CONTINUOUS WAVELET TRANSFORM

2016 ◽  
Vol 10 (1) ◽  
pp. 3-10
Author(s):  
Celso A. G. Santos ◽  
Richarde Marques Silva ◽  
Seyed Ahmad Akrami
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
River Basin ◽  
Continuous Wavelet Transform ◽  
Rainfall Data ◽  
Accurate Information ◽  
Rainfall Time Series ◽  
Continuous Wavelet ◽  
Rainfall Analysis ◽  
Frequency Components

The rainfall characteristics within Klang River basin is analyzed by the continuous wavelet transform using monthly rainfall data (1997–2009) from a raingauge and also using daily rainfall data (1998–2013) from the Tropical Rainfall Measuring Mission (TRMM). The wavelet power spectrum showed that some frequency components were presented within the rainfall time series, but the observed time series is short to provide accurate information, thus the daily TRMM rainfall data were used. In such analysis, two main frequency components, i.e., 6 and 12 months, showed to be present during the entire period of 16 years. Such semiannual and annual frequencies were confirmed by the global wavelet power spectra. Finally, the modulation in the 8–16-month and 256–512-day bands were examined by an average of all scales between 8 and 16 months, and 256 and 512 days, respectively, giving a measure of the average monthly/daily variance versus time, where the periods with low or high variance could be identified.

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